GeekDad Puzzle of the Week: Palindromic Sums of Squares

Are there more than 40 squares here?

If you have been on Facebook at all over the last year, you have probably seen the “puzzle” where there is a grid, and the question reads “How many squares do you see?” Some people (clearly not readers of this blog) only count the 1×1 squares, and not the 2×2, 3×3, 4×4 or larger squares.

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Some numbers, when squared, are palindromes: 112 is 121, and 262 is 676. Other numbers are the sums of sets of consecutive squares: 92 + 102 = 181, and 42 + 52 + 62 = 77.

This week’s puzzle is simple: How many numbers between 1 million and 10 million are both palindromes and the sums of sets of consecutive squares?

(NOTE: For purposes of this puzzle, please consider only sums of sets of squares of positive integers.)

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